test

doc/src/week45/week45.do.txt

@@ -377,6 +377,15 @@ plt.show()
 !ec
 
 
+Recall that the cumulative gains curve shows the percentage of the
+overall number of cases in a given category *gained* by targeting a
+percentage of the total number of cases.
+
+Similarly, the receiver operating characteristic curve, or ROC curve,
+displays the diagnostic ability of a binary classifier system as its
+discrimination threshold is varied. It plots the true positive rate against the false positive rate.
+
+
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 ===== Compare  Bagging on Trees with Random Forests  =====
 !bc pycod
@@ -811,6 +820,10 @@ and find a new value for $\rho_2=-1/2$ and continue till we have reached $m=M$.
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 ===== Gradient Boosting, algorithm =====
 
+Steepest descent is however not much used, since it only optimizes $f$ at a fixed set of $n$ points,
+so we do not learn a function that can generalize. However, we can modify the algorithm by
+fitting a weak learner to approximate the negative gradient signal. 
+
 Suppose we have a cost function $C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i))$ where $y_i$ is our target and $f(x_i)$ the function which is meant to model $y_i$. The above cost function could be our standard  squared-error  function
 !bt
 \[
@@ -826,10 +839,6 @@ o For $m=1:M$, we
   o update the estimate $f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x)$;
 o The final estimate is then $f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x)$.
 
-!split
-===== Gradient Boosting Example, Regression =====
-
-We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. 
 
 
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